Re: Relative Cardinality



Virgil wrote:

> > By the way, your definition of infinity would also make the values of
> > natural numbers infinite, because they are not bounded by any fixed
> > number n_0.
>
> WRONG! WM conflates infinitely many with infinitely large. There are
> infinitely many rationals in any non-degenerate real interval, but in
> bounded intervals, none of them are infinitely large, so that nfinitely
> many does not imply infinitely large.

I spoke of natural numbers.

If you represent the natural numbets in the unal system, i.e., 3 = III
etc, then there are as many strokes as there are numbers. Neither gets
infinite without the other.
>
> And even unboundedly large does not require infinitely large, as there
> are no infinitely large rationals or reals, though both are unbounded.

Regards, WM

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